 "Solutions to the RH and related mathematical research areasDisclaimer: with the exception of the last section E all papers of this page are without authorization from the ivory tower
for the latest updated version see http://www.fuchsbraun.com A. A Kummer function based Zeta function theory to prove the Riemann Hypothesis
http://www.riemannhypothesis.de
B. A global unique weak H(1/2) based variational representation of the 3D NavierStokes equation solution & a corresponding solution technique to prove the nonlinear Landau damping phenomenon
C. An alternative Schrödinger momentum operator and a related new ground state energy model of the harmonic quantum oscillator enabling a quantum gravity (NMEP) model
Abstract
We provide a new ground state energy model which ensures convergent quantum oscillator energy series. This enables the definition of a truly infinitesimal geometry based on a nonordered, still Archimedian field. The corresponding inner product with its induced norm defines the appropriate metric. The (Hilbert space) domains of related selfadjoint, positive definite operators to build appropriate eigenpair structures are built on Cartan´s differential forms. By this, H. Weyl´s "truly" infinitesimal (affine connexions, parallel displacements, differentiable manifolds based) geometry is replaced by a truly infinitesimal (rotation group based) geometry (corresponding to continuous manifolds, only). It is enabled by a new ly proposed H(1/2) Hilbert space based ground state energy model of the harmonic quantum oscillator:
D. Supporting papers
Braun K., "An alternative quantization of H=xp"
http://www.fuchsbraun.com/media/e9ed39ef818176fffff8031fffffff2.pdf
E. PhD thesis
The paper includes a proof of the quasioptimal approximation behavior of the RitzGalerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (PseudoDifferential) integral operator. Other examples would be the CalderonZygmund (singular integral) operator or the Hilbert transform (singular integral) operator.
